Holographic Magnetisation Density Waves

TL;DR

This paper constructs holographic models of magnetisation density waves in 3D conformal field theories, revealing a second-order phase transition to inhomogeneous current density states under magnetic fields.

Contribution

It introduces new numerical solutions of Einstein-Maxwell-scalar theories that demonstrate spontaneous formation of magnetisation density waves in holography.

Findings

Inhomogeneous magnetisation density waves form below a critical temperature.

The phase transition can be second order.

The stress tensor of the solutions resembles a perfect fluid.

Abstract

We numerically construct asymptotically $AdS$ black brane solutions of $D=4$ Einstein theory coupled to a scalar and two $U(1)$ gauge fields. The solutions are holographically dual to $d=3$ CFTs in a constant external magnetic field along one of the $U(1)$'s. Below a critical temperature the system's magnetisation density becomes inhomogeneous, leading to spontaneous formation of current density waves. We find that the transition can be of second order and that the solutions which minimise the free energy locally in the parameter space of solutions have averaged stressed tensor of a perfect fluid.